Determinantal Point Process (DPP): DPP [1]} is a probability distribution over power set of a ground set \(\mathcal {G}\) , here finite. DPP is a special case of negatively associated distributions [2]} which assigns higher probability mass on diverse subsets. Formally, a DPP with a marginal kernel \(L\)  (\(\in \mathbb {R}^{|\mathcal {G}| \times |\mathcal {G}|}\) ) is:
\(\mathbb {P}[\mathbf {Y}=Y] = \frac{\det (L_Y)}{\det (L+I)}\) , where \(Y \subseteq \mathcal {G}\)  and \(L_Y\)  is the principal submatrix defined by the indices of \(Y\) . We use \(k\) -DPP to denote the probability distribution over subsets of fixed size \(k\) .
